The shares, however, look overpriced Wednesday after rallying 4.20 to 23.70, a 21% gain in mid-morning trading.

The mobile shift continues to pose significant challenges to the company that isn't reflected in its richly valued shares. Facebook now trades for 49 times estimated 2012 profits of 48 cents a share and 38 times projected 2013 earnings of 62 cents a share.

Those P/Es are understated because of the company's heavy stock-based compensation that analysts exclude from their "pro-forma" earnings calculations. These charges for restricted stock total about 20 cents a share annually. Virtually all companies outside the technology sector don't pretend, as Facebook does, that the valuable restricted stock doled out to employees isn't an expense.

Facebook yesterday reported pro-forma earnings of 12 cents a share, a penny above Street expectations. Some analysts lifted their 2012 and 2013 earnings estimates by a few cents. Facebook shares are up about 5% since our bearish cover story last month (See "Still Too Pricey," Sept. 24, 2012).

Bank of America Merrill Lynch analyst Justin Post lifted his rating on Facebook to Buy from Neutral, writing in a client note that "while we were cautious on Facebook's mobile transition and expectations built into valuation" when he initiated coverage of the company in June "3Q results suggest that FB can effectively grow revenues while usage transitions to mobile platforms from PC." He lifted his price target to $31 from $23.

Facebook said mobile now accounts for about 20% of its ad revenues and that mobile ad revenues are running at $3 million a day, up from $500,000 a day in the second quarter. Total revenues were $1.26 billion, up 32% from a year earlier.

While mobile ad revenue was up smartly, desktop ad growth slowed, rising 17% in the third quarter from a year earlier, down from 26% in the second quarter and 37% in the first quarter. Some of the growth in mobile ads appears to be coming at the expense of the desktop. Payment trends, keyed-off games played by Facebook users on PCs, also has been soft

One key issue is whether Facebook has been aggressively pushing mobile ads, known as sponsored stories, in users' news feeds in an effort to convince Wall Street that it is serious about monetizing its platform and justifying its lofty valuation. Analyst Richard Greenfield of BTIG has been critical of Facebook's mobile ad strategy, writing yesterday that "we have yet to see any kind of sophisticated targeting on the platform." The mobile ads are more prominent than those on PCs, which may alienate users who could view them more like spam than anything useful.

Greenfield wonders whether the rate of accidental "Likes" has increased with the mobile shift thanks to the "fat finger" problem of users making accidental clicks on a small screen. "We view this as a critical issue, as accidentally clicking on an ad on most mobile websites causes you to see an unwanted ad, but clicking Like accidentally on Facebook causes you and all or your friends to be spammed by that brand daily going forward."

With the gain in the stock price today, Facebook is valued at about $65 billion. That's a lot for a company whose revenues are averaging about $5 billion a year.